It should be recalled that the purpose of such precoding is firstly to cause the signals that are transmitted by the transmit antenna(s) to be focused onto the receive antennas, and secondly to maximize the data rate between the transmitter and the receiver, for given power at the transmitter.
Strictly speaking, an aspect of the present invention relates to a single carrier system for transmitting data over a channel that is “flat” in frequency space, i.e. without echoes, also known as “flat fading”. In this particular situation, the propagation channel between any transmit antenna and any receive antenna may be represented merely by a complex gain, which is measurable. Consequently, the propagation channel between an array of a plurality of transmit antennas and an array of a plurality of receive antennas can be represented by a measurable complex matrix in which each row corresponds to a receive antenna and each column to a transmit antenna.
Under such circumstances, the aspects of the invention may advantageously be applied to each of the subcarriers of a multicarrier system, such as modulation making use of orthogonal frequency division multiplexing (OFDM), which can be reduced to S independent single-carrier systems (where S is the number of subcarriers), each transmitting over a propagation channel that is flat in frequency space, and each being capable of implementing aspects of the present invention.
In this respect, it should be recalled that the radio signal transmitted by a transmit antenna is subjected to deformation as a function of the propagation conditions between the transmit antenna and a receive antenna. In order to limit this deformation, the signal is distorted before transmission by applying so-called “pre-equalization” coefficients as a function of the characteristics of the propagation channel between the two antennas. In order to be able to do this, it is therefore necessary to be able to determine the characteristics of the propagation channel in the frequency band in question.
Among existing pre-equalization methods, methods making use of the so-called “time reversal” technique stand out because of its reduced complexity, its good performance, and its intrinsic ability to focus a radio wave on a receive antenna. Time reversal makes it possible for the dispersion caused by the propagation channel to be reduced significantly by focusing the energy of the transmitted signal both in time and in space.
Time reversal is a technique that was originally used in the field of soundwaves and that relies on the wave equation being invariant with respect to time reversal. Thus, a time-reversed wave propagates like a direct wave going backwards in time. When a short pulse transmitted from an origin point propagates through a propagation medium, and a portion of this wave as received by a destination point is time reversed prior to being sent back through the propagation medium, then the time-reversed wave converges on the origin point where it reconstitutes a short pulse. The signal picked up at the origin point is practically identical in waveform to the original signal transmitted from the origin point.
The time reversal technique has been applied to radio communications networks for canceling the effect of the propagation channel on the signal received by a receive antenna, in particular by reducing the spread of the channel by concentrating energy on a focal point where the receive antenna is located and by reducing the spread in time, known as the “delay spread” of the received signal, and also for simplifying the processing of received symbols after they have passed through the channel. For this purpose, the signal transmitted by a transmit antenna is pre-equalized by applying coefficients that are obtained on the basis of time reversal of the impulse response of the propagation channel over which the signal is to pass.
With TDD transmission, the reciprocity of the channel enables the transmitter to estimate the channel with the help of pilot signals. The receiver transmits pilot signals, and the transmitter estimates the propagation channel, with the transmitter then using its estimate to pre-equalize the data signal before transmitting it.